package prefuse.util.collections;

/**
 * Not of interest for users; only for implementors of hashtables. Used to keep
 * hash table capacities prime numbers.
 * 
 * <p>
 * Choosing prime numbers as hash table capacities is a good idea to keep them
 * working fast, particularly under hash table expansions.
 * </p>
 * 
 * <p>
 * However, JDK 1.2, JGL 3.1 and many other toolkits do nothing to keep
 * capacities prime. This class provides efficient means to choose prime
 * capacities.
 * </p>
 * 
 * <p>
 * Choosing a prime is <tt>O(log 300)</tt> (binary search in a list of 300
 * int's). Memory requirements: 1 KB static memory.
 * </p>
 * 
 * This class has been adapted from the corresponding class in the COLT
 * library for scientfic computing.
 * 
 * @author wolfgang.hoschek@cern.ch
 * @version 1.0, 09/24/99
 */
public class PrimeFinder extends Object {
    /**
     * The largest prime this class can generate; currently equal to
     * <tt>Integer.MAX_VALUE</tt>.
     */
    public static final int largestPrime = Integer.MAX_VALUE; // yes, it is
                                                              // prime.

    /**
     * The prime number list consists of 11 chunks. Each chunk contains prime
     * numbers. A chunk starts with a prime P1. The next element is a prime P2.
     * P2 is the smallest prime for which holds: P2 >= 2*P1. The next element is
     * P3, for which the same holds with respect to P2, and so on.
     * 
     * Chunks are chosen such that for any desired capacity >= 1000 the list
     * includes a prime number <= desired capacity * 1.11 (11%). For any desired
     * capacity >= 200 the list includes a prime number <= desired capacity *
     * 1.16 (16%). For any desired capacity >= 16 the list includes a prime
     * number <= desired capacity * 1.21 (21%).
     * 
     * Therefore, primes can be retrieved which are quite close to any desired
     * capacity, which in turn avoids wasting memory. For example, the list
     * includes 1039,1117,1201,1277,1361,1439,1523,1597,1759,1907,2081. So if
     * you need a prime >= 1040, you will find a prime <= 1040*1.11=1154.
     * 
     * Chunks are chosen such that they are optimized for a hashtable
     * growthfactor of 2.0; If your hashtable has such a growthfactor then,
     * after initially "rounding to a prime" upon hashtable construction, it
     * will later expand to prime capacities such that there exist no better
     * primes.
     * 
     * In total these are about 32*10=320 numbers -> 1 KB of static memory
     * needed. If you are stingy, then delete every second or fourth chunk.
     */
    private static final int[] primeCapacities = {
            // chunk #0
    largestPrime,

            // chunk #1
    5, 11, 23, 47, 97, 197, 397, 797, 1597, 3203, 6421, 12853, 25717, 51437, 102877, 205759, 411527, 823117, 1646237, 3292489, 6584983, 13169977, 26339969, 52679969, 105359939, 210719881, 421439783, 842879579, 1685759167,

            // chunk #2
    433, 877, 1759, 3527, 7057, 14143, 28289, 56591, 113189, 226379, 452759, 905551, 1811107, 3622219, 7244441, 14488931, 28977863, 57955739, 115911563, 231823147, 463646329, 927292699, 1854585413,

            // chunk #3
    953, 1907, 3821, 7643, 15287, 30577, 61169, 122347, 244703, 489407, 978821, 1957651, 3915341, 7830701, 15661423, 31322867, 62645741, 125291483, 250582987, 501165979, 1002331963, 2004663929,

            // chunk #4
    1039, 2081, 4177, 8363, 16729, 33461, 66923, 133853, 267713, 535481, 1070981, 2141977, 4283963, 8567929, 17135863, 34271747, 68543509, 137087021, 274174111, 548348231, 1096696463,

            // chunk #5
    31, 67, 137, 277, 557, 1117, 2237, 4481, 8963, 17929, 35863, 71741, 143483, 286973, 573953, 1147921, 2295859, 4591721, 9183457, 18366923, 36733847, 73467739, 146935499, 293871013, 587742049, 1175484103,

            // chunk #6
    599, 1201, 2411, 4831, 9677, 19373, 38747, 77509, 155027, 310081, 620171, 1240361, 2480729, 4961459, 9922933, 19845871, 39691759, 79383533, 158767069, 317534141, 635068283, 1270136683,

            // chunk #7
    311, 631, 1277, 2557, 5119, 10243, 20507, 41017, 82037, 164089, 328213, 656429, 1312867, 2625761, 5251529, 10503061, 21006137, 42012281, 84024581, 168049163, 336098327, 672196673, 1344393353,

            // chunk #8
    3, 7, 17, 37, 79, 163, 331, 673, 1361, 2729, 5471, 10949, 21911, 43853, 87719, 175447, 350899, 701819, 1403641, 2807303, 5614657, 11229331, 22458671, 44917381, 89834777, 179669557, 359339171, 718678369, 1437356741,

            // chunk #9
    43, 89, 179, 359, 719, 1439, 2879, 5779, 11579, 23159, 46327, 92657, 185323, 370661, 741337, 1482707, 2965421, 5930887, 11861791, 23723597, 47447201, 94894427, 189788857, 379577741, 759155483, 1518310967,

            // chunk #10
    379, 761, 1523, 3049, 6101, 12203, 24407, 48817, 97649, 195311, 390647, 781301, 1562611, 3125257, 6250537, 12501169, 25002389, 50004791, 100009607, 200019221, 400038451, 800076929, 1600153859

    /*
     * // some more chunks for the low range [3..1000] //chunk #11
     * 13,29,59,127,257,521,1049,2099,4201,8419,16843,33703,67409,134837,269683,
     * 539389,1078787,2157587,4315183,8630387,17260781,34521589,69043189,138086407,
     * 276172823,552345671,1104691373,
     * 
     * //chunk #12 19,41,83,167,337,677,
     * //1361,2729,5471,10949,21911,43853,87719,175447,350899,
     * //701819,1403641,2807303,5614657,11229331,22458671,44917381,89834777,179669557,
     * //359339171,718678369,1437356741,
     * 
     * //chunk #13 53,107,223,449,907,1823,3659,7321,14653,29311,58631,117269,
     * 234539,469099,938207,1876417,3752839,7505681,15011389,30022781,
     * 60045577,120091177,240182359,480364727,960729461,1921458943
     */
    };

    static { // initializer
        // The above prime numbers are formatted for human readability.
        // To find numbers fast, we sort them once and for all.
        java.util.Arrays.sort(primeCapacities);
    }

    /**
     * Makes this class non instantiable, but still let's others inherit from
     * it.
     */
    protected PrimeFinder() {
    }

    /**
     * Returns a prime number which is <code>&gt;= desiredCapacity</code> and
     * very close to <code>desiredCapacity</code> (within 11% if
     * <code>desiredCapacity &gt;= 1000</code>).
     * 
     * @param desiredCapacity
     *            the capacity desired by the user.
     * @return the capacity which should be used for a hashtable.
     */
    public static int nextPrime(int desiredCapacity) {
        int i = java.util.Arrays.binarySearch(primeCapacities, desiredCapacity);
        if (i < 0) {
            // desired capacity not found, choose next prime greater than
            // desired capacity
            i = -i - 1; // remember the semantics of binarySearch...
        }
        return primeCapacities[i];
    }

} // end of class PrimeFinder
